A function that represents the balance y (in dollars) of the investment account after t year is y = $120 × (1 + 0.064/4)^(4t).
The balance of an investment account is the sum of all deposits and withdrawals to/from an investment account, considering the manager's compensation calculation.
After the trading interval ends and compensation is paid out, the account balance will equal the equity.
Let y be the investment account balance (in dollars) after t years. Then,
y = $120 × (1 + 0.064/4)^(4t)
Where the interest rate is 6.4% and is compounded quarterly.
So the interest rate per quarter is 0.064/4.
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5 out of 7 students in my class are car riders, the rest are bus riders. If 12 students in my class are bus riders, how students are there IN ALL?
9, 7, 21, 4
Answer:
42 students
Step-by-step explanation:
5 out of 7 students are car riders. This means 2 out of 7 students are bus riders. 12 students are bus riders.
12 = 2x/7, where x is the total number of students.
So, 84 = 2x
This means that x = 42. 2/7 of 42 is 12 so this is correct.
please solve this I'll mark brainliest
Answer:
Height = 100 cm.
Surface Area = 625 cm^2.
Step-by-step explanation:
The volume of the cube is identical to the volume of the cuboid.
Volume of the cube = 5^3 and volume of cuboid is base area * height.
5^3 = 2.5 * 0.5 * h (where h is the height of the cuboid).
h = 5^3/1.25
= 100 cm.
The surface area is:
A = 2 * area of base + 2 * area of 1 side + 2 area of other side
= 2 * 1.25 + 2* 100 * 0.5 + 2 * 100 * 2.5
= 2.5 + 100 + 500
= 602.5 m^2.
Go math lesson 4-2 constant rate of change. Pg 29
The equation to represent the given table is y=27x.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
From the table:
a) Proportional
2/54 = 3/81
1/27 =1/27
Yes, the number of tickets and total cost are Proportional
b) Using coordinates (2, 54) and (3, 81)
m=(81-54)/(3-2)
m=27
Substitute m=27 and (x, y)=(2, 54) in y=mx+c, we get
54=27(2)+c
c=0
Substitute m=27 and c=0 in y=mx+c, we get
y=27x
So, the equation is y=27x
c) Number of tickets are 14
d) Total cost = $378
Therefore, the equation to represent the given table is y=27x.
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which of the numbers are divisible by 4. 16, 20, 33, 64, 80, 95, 97, 105, 214, 216, 324, 405
Kenton compared gas mileage for three cars.
Car A—450 miles for 15 gallons
Car B—651 miles for 21 gallons
Car C—598 miles for 23 gallons
Which car has the best rate of miles per gallon?
Car A has the best rate at 30 miles per gallon.
Car B has the best rate at 31 miles per gallon.
Car C has the best rate at 26 miles per gallon.
All three cars had the same rate of miles per gallon.
Answer:
Car B has the best rate
Step-by-step explanation:
A: 450 mi / 15 gal = 30 mi/gal
B: 651 mi / 21 gal = 31 mi/gal
C: 598 mi / 23 gal = 26 mi/gal
31 > 30 > 26
Answer:Car B has the best rate at 31 miles per gallon
Step-by-step explanation: i did my math
What is the length of AB?
Answer:4
Step-by-step explanation:
because it is a right triangle so if cb is 2 that makes ac 2 then if you just look at the ab line it’s actually longer so it’s 4 ;)
which compact sets does there exist a number m such taht every open cover contains a finite subcover of m elemens
The unit interval [0,1] in the real numbers is a compact set, and we can find a number m such that every open cover of [0,1] contains a finite subcover of m elements.
A compact set is a set that satisfies the finite subcover property, which means that every open cover of the set contains a finite subcover. This means that for any open cover of a compact set, there exists a finite subcover containing a certain number of elements (m) that can cover the entire set.
Examples of compact sets that satisfy this property include closed and bounded sets in a metric space, such as closed intervals in real numbers, and closed and bounded subsets of Euclidean space.
The unit interval [0,1] in the real numbers is a compact set, and we can find a number m such that every open cover of [0,1] contains a finite subcover of m elements.
Other examples of compact sets are the closed unit ball in a Euclidean space, and any finite set, where the number m would be equal to the number of elements in the set.
In summary, compact sets are sets that have the property of finite subcover, and for any open cover of a compact set, there exists a finite subcover containing a certain number of elements (m) that can cover the entire set. Some examples of compact sets are closed and bounded sets in a metric space, closed intervals in real numbers, closed and bounded subsets of Euclidean space, closed unit balls in Euclidean space, and any finite set.
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a swimming pool had 2.5 million liters some of the water evaporated and now the pool had 2 million liters of water what percent of water evaporated.
show all work
Answer:
4/5 = .8. 20% evaporated
Step-by-step explanation:
2.5 million divded into fifth. you have 5/5
take away half a million and that is 1/5th
at the end you have 4/5th left
4/5 = .8 = 80% left over meaning 20% evaporated
The height of a kicked ball can be modeled by the quadratic function h = - 0.01x^2 + 1.18x + 2. The horizontal distance traveled by the ball in feet is represented by x, and h is the height of the ball in feet. Approximately how far does the ball travel horizontally by the time it hits the ground?
The horizontal distance of the ball when it hits the ground is equal to 119.671 feet.
How to determine the horizontal distance traveled by the ball when it hits the ground
According to statement, we find the equation of the path covered by the ball, that is, a quadratic equation of the height of the ball (h), in feet, in terms of horizontal distance (x), in feet. In this case we need to determine a value of x greater than zero such that h = 0, that is to say:
- 0.01 · x² + 1.18 · x + 2 = 0
The roots of the quadratic equation can be found easily by quadratic formula:
x = - 1.18 / [2 · (- 0.01)] ± [1 / [2 · (- 0.01)]] · √(1.18² - 4 · (- 0.01) · 2)
x = 59 ± 60.671
The only realistic solution for the horizontal distance of the ball is x = 59 + 60.671 = 119.671 feet.
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The prices paid for a model of a new car are approximately normally distributed with
a mean of $17,000 and a standard deviation of $500.
The price that is 3 standard deviations above the mean is $
The price that is 2 standard deviations below the mean is $
The percentage of buyers who paid between $16,500 and $17,500 is
The percentage of buyers who paid between $17,000 and $18,000 is
The percentage of buyers who paid less than $16,000 is
a) The price that is 3 standard deviations above the mean is $18500
b) The price that is 2 standard deviations below the mean is 16000
c) The percentage of buyers who paid between $16,500 and $17,500 is 68%.
d) The percentage of buyers who paid between $17,000 and $18,000 is
47.5%
e) The percentage of buyers who paid less than $16,000 is 2.5%.
What is Standard Deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
Mean= 17000
standard deviation = $500.
a) The price that is 3 standard deviations above the mean is $
= 17000 + 3 x 500
= 18500
b) The price that is 2 standard deviations below the mean is $
= 17000 - 2 x 500
= 16000
c) The percentage of buyers who paid between $16,500 and $17,500 is
As, This is the bell curve numbers of 1 deviation which 68%.
d) The percentage of buyers who paid between $17,000 and $18,000 is
So, 1/2 of the 2nd deviation, or 95% x 0.5
= 47.5%
e) The percentage of buyers who paid less than $16,000 is 5% is outside of the 2nd deviation which is half of that or 2.5%.
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El primo de la señora Martha fue a pedir un préstamo de $1800 bajo las mismas condiciones que la señora Martha ¿cuánto pagara de interés en primo de la señora Martha?
Mrs. Martha's cousin will pay $108 in interest for a loan of $1800.
What is interest in a simple definition?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.Interest is the money you owe when borrowing or receive when lending. Lenders calculate interest as a percentage of the loan amount. Consumers can earn interest by lending money (such as through a bond or certificate of deposit) or depositing funds into an interest-bearing bank account.The three types of interest include simple (regular) interest, accrued interest, and compounding interest.Since Mrs. Martha is paying an interest rate of 6% per year, her cousin will also pay 6% per year.
To calculate the amount of interest paid, we can use the formula:
Interest = Principal * Rate * Time
Where:
Principal = $1800Rate = 6% (or 0.06 as a decimal)Time = 1 yearSo:
Interest = $1800 * 0.06 * 1 = $108
Therefore, Mrs. Martha's cousin will pay $108 in interest for a loan of $1800.
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How much must a carpenter cut off a 48-inch board if the length must
be 40 ± 0.25 inches?
Answer:
Step-by-step explanation:
let 'x' represent the amount removed, then we require:
40-0.25 <= 48-x <= 40+0.25
which solves to:
7.75 <= x <= 8.25
the carpenter must saw off between 7.75 and 8.25 inches
I added a picture below
If the final statement when solving a system of linear equations is "5 = 0", it means that: E. none of these statements are true.
What is the Solution to a System of Linear Equations?A solution to a system of linear equations is a set of values for the variables that satisfy all the equations in the system simultaneously. In other words, it is a collection of values for the variables that make all the equations in the system true at the same time.
The solution can be represented graphically as the intersection of the lines or planes defined by the equations in the system, or it can be represented algebraically as a set of values for the variables.
The equation "5 = 0" is false. It means that 5 cannot be equal to 0. This could indicate that the system of linear equations has no solution or that there is an error in the method being used to solve it.
Therefore, the answer is: "none of these statements are true".
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Find the measure of each acute angle.
Answer:
Step-by-step explanation:
The sum of the angles in a triangle is 180
So, (19x-1)+(13x-5)+90(right angle) =180
32x+84=180
32x=96
x=3
19x3-1=56
13x3-5=34
answer : 56, 34
there are $20$ cars in my building's parking lot. all of the cars are red or white. also, all the cars are either $2$-door or $4$-door. $12$ of them are red, $15$ of them are $4$-door, and $4$ of them are $2$-door and white. how many of the cars are $4$-door and red?there are $20$ cars in my building's parking lot. all of the cars are red or white. also, all the cars are either $2$-door or $4$-door. $12$ of them are red, $15$ of them are $4$-door, and $4$ of them are $2$-door and white. how many of the cars are $4$-door and red?
There are a total of 20 cars average in the parking lot, all of which are either red or white and either 2-door or 4-door. 12 of the cars are red, 15 of them are 4-door, and 4 of them are 2-door and white. Out of the 12 red cars, 12 of them are 4-door, so the answer is 12 cars are 4-door and red.
1. Determine the total number of cars in the parking lot: 20
2. Subtract the number of 2-door cars from the total number of cars to get the number of 4-door cars:
20 - 4 = 15
3. Subtract the number of 2-door and white cars from the number of red cars to get the number of 4-door and red cars:
12 - 4 = 8
4. Add the number of 4-door and red cars to the number of 4-door cars to get the answer:
8 + 15 = 12
To find the answer, we first determined the total number of cars in the parking lot, which was 20. We then subtracted the number of 2-door cars from the total number to get the number of 4-door cars, which was 15. We then subtracted the number of 2-door and white cars from the number of red cars to get the number of 4-door and red cars, which was 8. Finally, we added the number of 4-door and red cars to the number of 4-door cars to get the answer, which was 12.
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Find the outputs a and b needed to satisfy the consumer and interindustry demands given in the following figure. See Exercise 24:
The output a needed to satisfy the consumer and interindustry demands is 12 units, and the output b needed to satisfy the consumer and interindustry demands is 6 number of units.
a) Output a = 12 (units)
b) Output b = 6 (units)
1. Calculate the total consumer demand (CD):
CD = 12 + 20 + 8 = 40 (units)
2. Calculate the total interindustry demand (ID):
ID = 4 + 5 + 9 = 18 (units)
3. Calculate the total production (TP):
TP = CD + ID = 40 + 18 = 58 (units)
4. Calculate the output a and b needed to satisfy the consumer and interindustry demands:
a) Output a = TP - ID = 58 - 18 = 40 (units)
b) Output b = CD - Output a = 40 - 12 = 28 (units)
The output a needed to satisfy the consumer and interindustry demands is 12 units, and the output b needed to satisfy the consumer and interindustry demands is 6 number of units.
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2 pound into ounces
Answer: 32 oz
Step-by-step explanation:
Answer: 32
Step-by-step explanation: a pound is 16 ounces
The volume of a rectangular prism with sides 3 ft, 4 ft, and h ft must be at least 36 cubic ft. write and solve an inequality that represents the value of h. please help give brainliest for best answer!!!! its due in 20 minutes
use the form of inequality; answer
ex. 180x<360; x<2
An inequality that represents the value of height h of rectangular prism is h ≤ 3
We know that the formula for the volume of a rectangular prism,
V = l × w × h
where l is the length of the rectangular prism,
w is the width of the rectangular prism
and h is the height of the rectangular prism
Here, we ahve been given a rectangular prism with sides 3 ft, 4 ft, and h ft
l = 4 ft, w = 3 ft
The volume of a rectangular prism with sides 3 ft, 4 ft, and h ft must be at least 36 cubic ft.
V ≥ 36
Using the formula of the volume of a rectangular prism we get an inequality,
l × w × h ≥ 36
4 × 3 × h ≥ 36
We solve an inequality that represents the value of h.
12 × h ≥ 36
Divide both sides by 36
(12h/12) ≥ (36/12)
h ≥ 3
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Consider the parent function f (x) below.
1. Graph f(2x) in the color green below.
2. Graph -3f(x) in the color blue below.
3. Graph 2f (2x) in the color red below.
The graph of all the functions are given below.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
From the graph:
The parent function f(x) = eˣ.
The graph of the parent function is given the attached image in purple line.
So,
1). f(2x) = e²ˣ
Graph f(2x) in the color green below.
2). -3f(x) = -3 eˣ.
Graph -3f(x) in the color blue below.
3). 2f(2x) = 2e²ˣ
Graph 2f (2x) in the color red below.
Therefore, all the graphs are given in the attached image.
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what do you think about the proposed new york city ban on sugary soft drinks larger than 16 ounces? think about both sides of the argument, and give pros and cons.
The proposed ban on sugary soft drinks larger than 16 ounces in New York City has both pros and cons. Pros include reducing obesity and diabetes, while cons include potential infringement on personal freedom and potential negative impact on small businesses.
The proposed ban on sugary soft drinks larger than 16 ounces in New York City aims to reduce obesity and diabetes by limiting the consumption of high-calorie beverages. This can also help to lower the healthcare costs associated with these conditions. However, some argue that this is an infringement on personal freedom and that people should have the right to make their own choices about what they eat and drink. Additionally, there are concerns that small businesses, such as convenience stores and vending machine operators, could be negatively impacted by the ban. This is because they may lose sales as a result of the ban, which could lead to job losses and financial hardship.
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What index of x will equal to 1/x^x
Answer:
The index of x should be 0 so that its value will be equal to 1.
Lena and Ivan each ran every day as part of an exercise routine. Lena ran 3 miles each day for x days. Ivan ran 4 miles each day for y days.
The total number of miles that Lena ran is at least the total number of miles that Ivan ran. Write an inequality describing this relationship.
The inequality that shows the distance ran is 3x ≥ 4y
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
Inequalities are used for the non equal comparison of numbers and variables.
Lena ran 3 miles each day for x days. Ivan ran 4 miles each day for y days.
Total number of miles that Lena ran = 3x
Total number of miles that Ivan ran = 4y
The total number of miles that Lena ran is at least the total number of miles that Ivan ran, hence:
3x ≥ 4y
The inequality is 3x ≥ 4y
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approximately what percentage of children will score within the average range of iq testing? group of answer choices 20% 37% 68% 85%
The required interval of the given normal distribution using the empirical rule is [100, 140].
The empirical rule formula (also known as a 68 95 99 rule formula) uses data from a normal distribution to determine the first, second, and third standard deviations, which, respectively, differ from the mean value by 68%, 95%, and 99%. Additionally, it shows that 99.9% of the data fall inside the third standard deviation range (either above or below the mean value). The empirical rule formula is described below with cases that have been resolved.
In the question, we are given that IQ scores for adults aged 20 to 34 years are normally distributed according to N(120, 20), and are asked for the range in which the middle 68% of people in this group score on the test.
N(120, 20) signifies a normal distribution with mean, μ = 120, and the standard deviation, σ = 20.
By the empirical formula, 68% of the data lies within one standard deviation from the mean.
Thus, the required interval is [μ - σ, μ + σ] = [120 - 20, 120 + 20] = [100, 140].
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ASHPREET buys two packages of plates and three packages of forks for the class party she gives the clerk $50 how much was the total. And how much did the clerk give back
The total that Ashpreet bought, given the price of the plates and the forks, is $ 16. 95
The amount that the clerk should give back, given the amount Ashpreet gave the clerk, is $ 33. 05
How to find the total amount ?The total amount that Ashpreet will pay for the two packages of plates and the packages of forks, given the price of the plates and the price of the forks is:
= ( Cost of plates x Number of packages of plates ) + ( Cost of forks x Number of plate packages )
= ( 5. 79 x 2 ) + ( 1. 79 x 3 )
= 11. 58 + $ 5. 37
= $ 16. 95
The amount that the clerk would therefore give back to Ashpreet is:
= Amount Ashpreet paid with - Cost
= 50 - 16. 95
= $ 33. 05
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The rest of the question is:
The price of the packages of napkins and forks is: napkins $ 5.79 and forks $1.79
Which table represents a linear function example?
On solving the provided question, we can say that Graph Onerepresents a linear equation.
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
Graph One
The graph is linear, commonly known as being in a straight line. Other graphs are not, though. Additionally, the range (y) of the tables is rising linearly every time, by a factor of.5 (1/2).
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What is the slope of a function called?
The term “slope of a function” is short for “slope of the graph of a function” for some particular value of the independent variable.
The linear function's slope. A slope is a measure of how steep a hill is. The same is true of a line's steepness. The ratio of the rise, which is the vertical change between two points, to the run, which is the horizontal change between those same two points, is known as the slope.
The derivative of a function is if it has one, the slope at any point. The slope of the line that is tangent to the curve there is another definition for it. In calculus class, you learn how to discover derivatives starting with limit theorems and moving on to numerous other "shortcut" theorems that make finding many derivatives easier.
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Given the diagram below solve for side b
The length of the hypotenuse of the right triangle is:
B = 24.4
How to find the length of side B?Side B is the side opposite to the angle B, so it will be the hypotenuse of the right triangle.
We know the other two sides of the right triangle, so we can use the Pythagorean theorem to get:
C^2 + A^2 = B^2
Replacing the values that we know:
A = 20
C = 14
We will get:
20^2 + 14^2 = B^2
√(20^2 + 14^2) = B
24.4 = B
That is the length of the hypotenuse
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During the first three hours of a recent storm the rain fell at a constant rate of 10 mm per hour. The storm stopped for the next 2 hours and then it started raining again at a constant rate of 20 mm per hour for the next 5 hours. Match the pieces of the piecewise function that describes the total rainfall in this situation with the appropriate domain.
f(h)=10h
f(h)=30
f(h)=30+20(h-5)
The total rainfall in this situation with the appropriate domain is f(h)=10h is 1-3 hours, f(h)=30 is 4 to 6 hours and f(h)=30+20(h-5) is 7 to 12 hours.
What is domain?The range of input values where a function can be defined, or the set of possible inputs, is known as the domain of the function. The domain is the collection of objects that the function machine will accept as inputs.
During the 1 to 3 hours, rain fell at a constant rate of 10 mm per hour, expressed as
f(h)=10h
During the 4 to 6 hours, rainfall is same, expressed as
f(h)=30
During the 7 to 12 hours, raining again at a constant rate of 20mm, expressed as
f(h)=30+20(h-5)
Thus, the total rainfall in this situation with the appropriate domain is f(h)=10h is 1-3 hours, f(h)=30 is 4 to 6 hours and f(h)=30+20(h-5) is 7 to 12 hours.
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Elsa will spend more than $25 on gifts. So far, she has spent $17. What are the possible additional amounts she will spend?
The required possible amount that she spends additionally is more than $8.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Elsa will spend more than $25 on gifts. So far, she has spent $17.
Let the possible additional amounts she will spend be x,
According to the quesiton,
x + 17 > 25
x > 25 - 17
x > 8
Thus, the required possible amount that she spends additionally is more than $8, as of the given condition.
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the three angles in a traingle are 5x, 6x and 7x. work out the size of the largest angle in the triangle
Answer:
the largest angle is 70
Step-by-step explanation:
180 degrees in a triangle
180=5x+6x+7x
simplify
180=18x
x=10
7x=70
the largest angle is 70 degrees.
